This thesis presents the experiments performed at the superconducting Darmstadt linear accelerator S-DALINAC to determine the longitudinal structure of the electron bunches. The operation of the free-electron laser at the accelerator requires to meet the design parameters, particularly the bunch length with 2 ps and the energy spread with lesser than 0.3 %. To measure the structure of the bunches two diagnostic stations have been constructed, where the millimeter wave spectra of coherent transition radiation can be obtained. Both spectrometers of Martin-Puplett type are designed with minimal space requirements to cover the spectral range between 5 mm and 0.3 mm, necessary for a determination of the bunch shape. The spectral sensitivity above 2.5 mm ist affected by diffraction. Therefore, this sensitivity was simulated by a multi-mode calculation to enable a reconstruction of the bunch shape. With measurements at both diagnostic stations the setup of the accelerator could be optimised to meet the required peak current for the FEL operation and to obtain lasing of the FEL. The bunch shapes reconstructed are accordantly to the results from prior simulations of the accelerator. Besides the diagnostic method in the frequency domain using transition radiation a setup to determine the bunch shape in the time domain has been constructed, which is based on the electro-optic sampling of the coulomb field of the electron beam with femtosecond laser pulses. To correlate the 2 ps long bunches of the electron beam with the less than 100 fs long pulses of a Ti:Sapphire laser, a feedback system was implemented with a timing jitter of the laser better than 5 ps. Inside a vacuum chamber behind the injector accelerator a ZnTe crystal was placed some millimeters beside the electron beam path to measure its birefringence, induced by the coulomb field of the beam and the pockels effect, with the laser beam also directed through the chamber. The sensitivity of the detector for the laser polarisation was 0.5e-5, which was a factor of 100 better than the signal expected from the design values of the accelerator and a factor of 10 better than the value estimated from beam parameters achieved during the experiment. A correlation signal between laser pulses and electron bunches could not be found. Future experiments for electro-optic sampling will take place at the accelerator of the TESLA test facility where due to a bunch charge of more than 1 nC a significantly higher effect can be expected. Currently, a setup to determine the electric field distribution of coherent transition radiation with electro-optic sampling is under construction.